In the figure shown below, chord ED is parallel to the diameter

AC of the circle. If $\angle CBE=60°$ , then what is the value of $\angle DEC?$

Join AB,AE,’AC’ Diameter.

$\therefore \angle ABC=90°$ (Angle in a Simi Circle)

Given that, $\angle CBE=60°$

$\therefore \angle ABE=\angle ABC-\angle CBE=90°-60°=30°$

$\therefore \angle ABE=\angle ACE=30°$ (Angles in a same Segment)

Now , AC||ED and CE is transversal

$\therefore \angle ACE=\angle DEC=30°$ (Alternate interior angles)

$\therefore \angle DEC=30°$